Multivariable Process Control (MPC) algorithms, e.g., Dynamic Matrix Control (DMC), require sufficiently accurate dynamic models of the process unit to ensure high performance control and maintain closed loop stability. The accuracy of the model places an upper limit on the obtainable closed loop performance of the multivariable control system. However, there is a finite limit imposed on the obtainable model accuracy. This is due to the approximation error introduced by representing the real process, which is often non-linear, with linear models, and the ability to identify the model through a system identification process based on observed process data that is usually corrupted by noise and disturbances.
In general, the most cost-effective way to derive accurate models of a large-scale process unit, is to vigorously perturb the process unit with suitable test signals without exceeding safety or operability constraints. The process perturbations have to cover the full amplitude and frequency range of the unit. Several different types of test signals can be used, including steps, pulses, random white noise sequences, of pseudo-random-binary (PRBS) signals. In the process control industry, step test signals are widely used because it is easy to generate these signals manually, and the procedure is referred to as step testing. For the purposes of this discussion, perturbing a process unit with the intent of identifying an empirical dynamic model, is referred to as step testing, whatever test signals are used.
Step testing consists of making sufficiently large orthogonal and independent step changes in all the manipulated variables (MV""s) of the process unit under careful supervision. Manipulated variables are those that are adjusted through actuators coupled to respective control valves, reactors, pumps/compressors, etc. forming the process unit and are for example feed rates, flow rate, temperature of a vessel, and the like. The step test data is then used in system identification algorithms to fit empirical dynamic models to the observed process responses. In order to minimize the duration and consequent cost of the step test, these step changes must be of sufficient amplitude to clearly observe the dynamic behavior of the process and maximize the signal to noise ratio. Correlation (dependence) between the MV""s has to be minimized to ensure that accurate models can be identified.
Model accuracy results from using large step changes, ensuring minimal correlation between MV""s and minimal feedback correlation, and ensuring that the step test sequence spans the full frequency range from very fast to very slow steps relative to the Time-to-Steady-State (TTSS) of the process. Unwanted feedback correlation results from the need to make frequent correcting moves in the MV""s to counteract the effect of large unmeasured disturbances, and can degrade the accuracy of the model.
Control valves must also be prevented from fully opening or closing (valve saturation), and tank levels must be kept within the range of the level measurement devices. The fast high frequency dynamics of the process model are important to ensure high performance closed loop control. The slow low frequency dynamics (or process gains) is important to ensure accurate prediction of the future steady-state operating point of the process. This ensures that the optimizer built into the MPC algorithm will determine the most economically optimum steady state targets for the various process variables, and the MPC control algorithm will maintain the process close to the optimum targets, resulting in substantial economic benefit.
It is also important to introduce enough large steps to ensure that the identification algorithm can average out the effect of unmeasured disturbances. The duration of the test is a direct result of the frequency content of the process output signals resulting from the test signals, relative to the frequency content of the process outputs resulting from unmeasured disturbances. Where the process model matrix has a dominantly diagonal model structure (i.e., several units connected in a series structure), independently perturbing several or even all inputs simultaneously can shorten the test duration. Essentially, the signal to noise ratio of every CV (controlled variable, e.g., temperature, pressure, composition, product properties, etc.) in every frequency range of interest has to be maximized.
A significant part of the cost of implementing MPC on major process units, is the cost associated with using highly trained control engineers to supervise the unit while step testing is in progress. The project team often has to supervise the unit on a 24 hours per day, 7 days per week basis to ensure that the step changes do not cause the process unit to exceed safety or operability constraints. Full supervision greatly increases the cost of implementing MPC on large process units with a large MV count, and/or a long time to steady state. The need for an automated algorithm to conduct the step testing of the process unit while ensuring safe operation and keeping all the products within quality specification, while guaranteeing good identification results, has been recognized for a long time and will provide a substantial competitive advantage to its inventor.
Previous Approaches
Several approaches have been used before and are described in the academic literature. Some are summarized next.
Manual Step Testing: Essentially, two or three highly skilled process control engineers working shifts around the clock introduce manual step changes usually in one independent variable at a time, while supervising the unit around the clock. Any unacceptable deviations in the dependent variable are corrected for by introducing additional steps to move the process back to the safe operating region (correcting moves). If the process control engineers are highly skilled, then this approach can provide acceptable data and sufficiently accurate models, but this is not always easy, and it can be very expensive. However, there is a natural tendency to make changes in a fixed order and to respond to process disturbances by making correcting moves. This inadvertently introduces correlation into the MV sequence and makes the model identification problematic. In practice, it is quite difficult to prevent valve saturation and loss of tank levels, the manual step test sequence does not usually have sufficient high frequency content, and step changes are kept small enough to prevent large deviations in the CV""s to reduce the risk of constraint violation. At present, this method is widely used in the process control industry.
Using a Programmed Step Test Sequence: This method relies on a sequence of carefully designed programmed step changes in every independent variable around a pre-defined average value, with the ability to manually adjust the average value and step size, or low and high limit values. Typically, the control engineer will choose a sequence based on process insight and good engineering practice to excite the fill frequency range of the process and ensure independence between the step test sequences. This method requires less intervention from the process control engineers once the sequence has been set up, but it still requires careful supervision, as the control engineer has to monitor the process closely, and move the average values when constraint violation occurs. High frequency content can be improved using this approach, but preventing valve saturation is still difficult. Once again, step change amplitudes are kept small enough to prevent excessive constraint violation, and it is still difficult to preventing loss of levels especially if automatic level controllers have to be disabled. This method can provide some improvements in terms of frequency content and reduced correlation, but does not reduce the cost of the project as full supervision is still required.
Using Pseudo Random Binary Sequences (PRBS): A PRBS sequence is automatically generated for every independent variable (MV). The PRBS method requires three parameters per independent variable (base period, amplitude, and sequence length). If these parameters are chosen appropriately, then the data will contain sufficient high frequency information. Since every independent variable will have a linearly independent sequence, all (or several of) the MV""s can be stepped at the same time. This has the advantage that any CV""s (controlled variables) that do not share the same MV""s, will be perturbed at the same time, potentially reducing the time required to generate sufficient data to fit accurate empirical models. If all the MV""s are perturbed at the same time, it is possible for the random sequence to occasionally generate steps in several of the MV""s that may cause deviation in the same direction. For this reason, the amplitude of the step changes have to be reduced by dividing the amplitudes that could have been used if only one independent variable was stepped at any one time, by the number of MV""s. This greatly reduces the amplitude of the steps, reducing the signal to noise ratio. Most process units are disturbed by large low frequency unmeasured disturbances, e.g. feed composition changes in chemical or refining process units. In such applications, a much larger amount of data has to be collected if small amplitudes have to be used. Full supervision is still required. Some cost advantage can be achieved due to a potentially shorter step test, but the need for careful supervision cannot be removed, limiting the achievable cost saving.
Superimposing PRBS Signals on top of Controller Outputs: A more sophisticated approach is to use a closed loop control system, e.g., an MPC system like DMC, and superimpose independent PRBS signals on top of every MV. The MPC controller will always respond by ramping out the pulse to return to the previous steady state targets. This modification generates sufficient medium to high frequency information, but it will not excite the low frequency dynamics of the process. In order to generate accurate gain estimates, large step changes in every limiting (or active) dependent variable has to be made, and at least some of these steps have to be maintained for the full TTSS. This improves the low frequency content of the data, but at the expense of a higher level of unwanted MV correlation. This approach has the advantage that it requires little or no supervision once a suitably accurate model has been determined. However, it has the disadvantage that an initial model needs to be available. A further more limiting disadvantage is the fact that all the MV""s will move in a highly correlated way. This can cause numerical difficulties for the system identification algorithm, leading to poor model accuracy. Another problem stems from feedback correlation appearing in the MV""s due to noise and disturbances in the CV""s, which also makes the system identification problem much more difficult. Since the controller responds to maintain the CV at their targets and limits, all the MV""s will exhibit correlation. The nearly ideal PRBS signals on each MV will be diluted by the correlation effect resulting from the control action. If the controller is slowly tuned, and large PRBS amplitudes are used, then the PRBS signal can swamp the controller action, in which case the data appears nearly open loop. Ideally, correlation between MV""s, and between CV""s and MV""s must be minimized as far as possible. Specifically, a high degree of feedback correlation due to high frequency noise and unmeasured disturbances is known to cause failure of multivariable model identification algorithms.
The previously mentioned method is substantially enhanced to overcome the stated problems and disadvantages. As before, an initial dynamic model is used to control the process. It is accepted that this model is not accurate enough for high performance process control, but if slow controller tuning and sufficiently over-conservative CV limits are used, the system can be set up to maintain stability, and reject external disturbances without violating the real process constraints.
Typically, only the major MV/CV responses are included in the initial model, and the sign of these responses must be correct. Where there is doubt about the gain and/or dead time of the model curves, it is safer to use higher rather than lower values. The ability of the initial model to serve as an adequate basis for controlling the process unit, is confirmed by making large programmed target and/or limit changes in every active CV. Where unstable and/or highly underdamped closed loop responses are observed, the CV steps can be repeated with only one major MV active at any time. In this way, the specific MV/CV pairs causing the poor closed loop response can be identified. It is then relatively straight-forward to increase the model gain in large steps (e.g. 2xc3x97) until acceptable performance is achieved. Where the closed loop performance is very slow due to unreasonably high model gains, the previous approach can once again be used to identify the responsible MV/CV pairs, and the model gain can be reduced in large steps until acceptable performance is achieved. The data collected during this procedure is of course highly correlated. However, this data can be combined with good quality independent and uncorrelated test data as long as the total amount of correlated data is less than approximately 20% of the total data set.
The system model can be improved periodically by importing the latest data and re-running the model identification. Where an initial model is not available, any of the existing testing methods can be used to generate a suitable initial model from only a small number of steps. An initial model of low to moderate accuracy is acceptable. For example, the initial model may be derived from a non-model based process control system, may be an existing model from a potentially different but similar process system, may be derived from a manual step test of the subject process being modeled, or may be derived from engineering knowledge of the subject process being modeled.
The previously mentioned approach where large programmed step changes are made in active CV targets can be used every few days to monitor model convergence and provide a stopping criterion. In this way, a large amount of system model identification and controller tuning and commissioning work can be accomplished in parallel with the step testing activities. Some of this work may also be done remotely via a high-speed communication link. These methodology enhancements can dramatically reduce the amount of engineering supervision required and the total cost of an MPC project.
In a preferred embodiment, the present invention method models a process system employing the steps of:
(a) modeling a subject process system with an initial model;
(b) coupling to the subject process system a multivariable process control system that utilizes said initial model, to control the subject process system;
(c) tuning said multivariable process control system for stable operation of the subject process system; and
(d) using data generated from said subject process system, generating an improved model of the subject process system, said steps of tuning and generating effectively perturbing the subject process system to generate data for model identification of the subject process system.
The steps (b) through (d) are repeated with the improved model as the initial model, such that a further improved model is generated. In a preferred embodiment, the multivariable process control system employs a constrained, model-based controller.
In accordance with one aspect of the present invention, the step of coupling to the subject process system includes computing process control action for controlled variables and manipulated variables following an objective function J. Preferably the objective function J is extremized.
Further the step of coupling to the subject process system includes augmenting the initial model with shadow system controlled variables. The shadow system controlled variables are mathematically and functionally equivalent to system manipulated variables which may be treated as system controlled variables. One or more of the system manipulated variables or shadow system controlled variables are moved or stepped simultaneously. In addition, one or more of the system manipulated variables or the shadow system controlled variables may be moved or stepped for desired amounts of time (either fixed or varying). In a preferred embodiment, a pseudo random binary (PRBS) sequence is superimposed on the moves or steps of the system manipulated variables and shadow system controlled variables.
In accordance with another aspect of the present invention, the gain relationship between a system manipulated variable and a system controlled variable is determined and normalized to unity. The multivariable process control system then utilizes the normalized gain relation as the shadow system controlled variable. Further the shadow system controlled variable targets are adjusted to prevent shadow system controlled variables from violating subject process control variable limits.
In accordance with another aspect of the present invention, the step of coupling to the subject process system includes constructing and controlling equivalent system manipulated variables. The values of the equivalent system manipulated variables are equal to the initial model predicted values when controlled variables of the subject process system are within subject process limits. Preferably the step of controlling equivalent system manipulated variables is in accordance with one of:
an objective function J;
a simultaneous moving of one or more shadow system controlled variables or system manipulated variables;
for an amount of time, moving of one or more shadow system controlled variables or system manipulated variables;
a superimposed PRBS sequence;
a normalized system manipulated variable-system controlled variable gain, the normalized gain being normalized to unity and used as the shadow system controlled variable; and
an adjustment of shadow system controlled variables targets to prevent shadow system controlled variables from violating subject process control variable limits.
In the preferred embodiment the step of coupling the subject process system includes imposing a dead zone on controlled variables of the multivariable process control system. The dead zone is computed by accumulating relatively small manipulated variable control action from the multivariable process control system. The control action is implemented when the summed control action reaches a predefined threshold. In addition, the controlled variables are filtered to attenuate high frequency noise.
In accordance with another aspect of the present invention, the step of coupling to the subject process system includes creating a time varying, almost periodic limit cycle of manipulated variables of the subject process system.
In accordance with another aspect of the present invention, suitable target values for the system manipulated variables of the subject process system are either chosen manually by a human operator or calculated by one of:
a middle value of process control limit values for controlled variables of the subject process system;
a partial least squares analysis;
a principle components analysis; and
a value furthest away from process control limit values of both manipulated variables and controlled variables of the subject process system.
Preferably the suitable targets for system manipulated variables are automatically determined and implemented by a digital processing system. In this manner a reduction of engineering supervision is enabled. Further the manipulated variables are stepped or moved in a random way about the suitable targets while keeping the manipulated variables and controlled variables of the subject process system within process control limits.
In accordance with another aspect of the present invention, the step of tuning the multivariable process control system includes adjusting internal variables of the multivariable process control system. The adjusting of internal variables is accomplished in a manner that improves process control action and ensures process system safety. Further the adjusting reduces feedback correlation between control action of the multivariable process control system and disturbances of the subject process system. The disturbances include unmeasured extraneous influences affecting the subject process system and not captured in the initial model.
In accordance with another aspect of the present invention, the step of using data and generating an improved model includes using a system identification algorithm and analyzing values of manipulated variables and controlled variables of the subject process system to create an improved model.
Apparatus for modeling a process system implements the foregoing method. Preferably computer means coupled to a multivariable process controller executes the method and effectively perturbs the subject process system to generate data for model identification.
Similarly a controller implements the foregoing method. The controller comprises a digital processor and a program storage device that is readable by the digital processor. The program storage device encodes a program of instructions for performing the method of modeling a subject process system. Other embodiments or applications of the invention method are in the purview of one skilled in the art having the following disclosure before him.